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%I #19 Sep 08 2022 08:44:49
%S 1,8,23,52,107,210,401,754,1405,2604,4811,8872,16343,30086,55365,
%T 101862,187385,344688,634015,1166172,2144963,3945242,7256473,13346778,
%U 24548597,45151956,83047443,152748112,280947631,516743310
%N a(n) = T(n, n+3), T given by A027052.
%H G. C. Greubel, <a href="/A027054/b027054.txt">Table of n, a(n) for n = 3..1002</a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (3,-2,0,-1,1).
%F From _Colin Barker_, Feb 19 2016: (Start)
%F a(n) = 3*a(n-1) - 2*a(n-2) - a(n-4) + a(n-5) for n>6.
%F G.f.: x^3*(1+5*x+x^2-x^3-2*x^4)/((1-x)^2*(1-x-x^2-x^3)). (End)
%F a(n) = A001590(n+4) -2*n -4, n>=3. - _R. J. Mathar_, Jun 15 2020
%p seq(coeff(series(x^3*(1+5*x+x^2-x^3-2*x^4)/((1-x)^2*(1-x-x^2-x^3)), x, n+1), x, n), n = 3..33); # _G. C. Greubel_, Nov 05 2019
%t LinearRecurrence[{3,-2,0,-1,1}, {1,8,23,52,107}, 30] (* _G. C. Greubel_, Nov 05 2019 *)
%o (PARI) my(x='x+O('x^33)); Vec( x^3*(1+5*x+x^2-x^3-2*x^4)/((1-x)^2*(1-x-x^2-x^3)) ) \\ _G. C. Greubel_, Nov 05 2019
%o (Magma) R<x>:=PowerSeriesRing(Integers(), 33); Coefficients(R!( x^3*(1+5*x+x^2-x^3-2*x^4)/((1-x)^2*(1-x-x^2-x^3)) )); // _G. C. Greubel_, Nov 05 2019
%o (Sage)
%o def A027053_list(prec):
%o P.<x> = PowerSeriesRing(ZZ, prec)
%o return P( x^3*(1+5*x+x^2-x^3-2*x^4)/((1-x)^2*(1-x-x^2-x^3)) ).list()
%o a=A027053_list(33); a[3:] # _G. C. Greubel_, Nov 05 2019
%o (GAP) a:=[1,8,23,52,107];; for n in [6..33] do a[n]:=3*a[n-1]-2*a[n-2] -a[n-4]+a[n-5]; od; a; # _G. C. Greubel_, Nov 05 2019
%K nonn,easy
%O 3,2
%A _Clark Kimberling_
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